Question

If the size of one interior angle of a regular polygon is 108° how many sides does the polygon have?

Answer 1

now, recall that the sum of all interior angles is 180(n-2), now, let's say one angle is θ, and there are "n" sides in the polygon, so if add up all the θ angles, what the sum will then be is just θn, or that product, therefore,


`\bf \theta n=180(n-2)\quad \begin{cases} \theta =angle~in\\ \qquad degrees\\ n=number~of\\ \qquad sides\\ -------\\ \theta =108 \end{cases}\implies 108n=180n-360 \\\\\\ 360=72n\implies \cfrac{360}{72}=n`

and surely you know how much that is.